Point clouds are a popular representation for 3D shapes. However, they encode a particular sampling without accounting for shape priors or non-local information. We advocate for the use of a hierarchical Gaussian mixture model (hGMM), which is a compact, adaptive and lightweight representation that probabilistically defines the underlying 3D surface. We present PointGMM, a neural network that learns to generate hGMMs which are characteristic of the shape class, and also coincide with the input point cloud. PointGMM is trained over a collection of shapes to learn a class-specific prior. The hierarchical representation has two main advantages: (i) coarse-to-fine learning, which avoids converging to poor local-minima; and (ii) (an unsupervised) consistent partitioning of the input shape. We show that as a generative model, PointGMM learns a meaningful latent space which enables generating consistent interpolations between existing shapes, as well as synthesizing novel shapes. We also present a novel framework for rigid registration using PointGMM, that learns to disentangle orientation from structure of an input shape.
Recent years have witnessed the emergence of 3D medical imaging techniques with the development of 3D sensors and technology. Due to the presence of noise in image acquisition, registration researchers focused on an alternative way to represent medical images. An alternative way to analyze medical imaging is by understanding the 3D shapes represented in terms of point-cloud. Though in the medical imaging community, 3D point-cloud processing is not a ``go-to'' choice, it is a ``natural'' way to capture 3D shapes. However, as the number of samples for medical images are small, researchers have u…
Deep point cloud registration methods face challenges to partial overlaps and rely on labeled data. To address these issues, we propose UDPReg, an unsupervised deep probabilistic registration framework for point clouds with partial overlaps. Specifically, we first adopt a network to learn posterior probability distributions of Gaussian mixture models (GMMs) from point clouds. To handle partial point cloud registration, we apply the Sinkhorn algorithm to predict the distribution-level correspondences under the constraint of the mixing weights of GMMs. To enable unsupervised learning, we design …
Stanford University（斯坦福大学）；MILA（蒙特利尔学习算法研究所）；University of Montréal（蒙特利尔大学）
Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with state-of-the-art reconstruction quality and generalization ability. The learned representations outperform existing methods on 3D recognition tasks and enable shape editing via simple algebraic manipulations, such as semantic part editing, shape analogies and shape interpolation, as well as shape completion. We perform a thorough study of different generati…
Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global probability alignment based on the convolution of adaptive Gaussian Mixture Models (GMM) from point clouds. Firstly, a novel adaptive GMM is defined using probability distributions from the corresponding points. Then rigid point cloud alignment is performed by maximizing the global probability from the convolution of dual adaptive GMMs in the whole 2D or 3D sp…
TerraNIS；University of Toulouse（图卢兹大学）；IRIT-INP-ENSEEIHT（图卢兹国立综合理工学院-ENSEEIHT-图卢兹计算机研究所）；TéSA（航空航天电信实验室）；IRIT-UPS（图卢兹第三大学-图卢兹计算机研究所）
Missing data is a recurrent problem in remote sensing, mainly due to cloud coverage for multispectral images and acquisition problems. This can be a critical issue for crop monitoring, especially for applications relying on machine learning techniques, which generally assume that the feature matrix does not have missing values. This paper proposes a Gaussian Mixture Model (GMM) for the reconstruction of parcel-level features extracted from multispectral images. A robust version of the GMM is also investigated, since datasets can be contaminated by inaccurate samples or features (e.g., wrong cr…
Point cloud registration sits at the core of many important and challenging 3D perception problems including autonomous navigation, SLAM, object/scene recognition, and augmented reality. In this paper, we present a new registration algorithm that is able to achieve state-of-the-art speed and accuracy through its use of a hierarchical Gaussian Mixture Model (GMM) representation. Our method constructs a top-down multi-scale representation of point cloud data by recursively running many small-scale data likelihood segmentations in parallel on a GPU. We leverage the resulting representation using …
National University of Singapore（新加坡国立大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Probabilistic point cloud registration methods are becoming more popular because of their robustness. However, unlike point-to-plane variants of iterative closest point (ICP) which incorporate local surface geometric information such as surface normals, most probabilistic methods (e.g., coherent point drift (CPD)) ignore such information and build Gaussian mixture models (GMMs) with isotropic Gaussian covariances. This results in sphere-like GMM components which only penalize the point-to-point distance between the two point clouds. In this paper, we propose a novel method called CPD with Loca…
University of Technology Sydney（悉尼科技大学）；Fondazione Bruno Kessler（布鲁诺·凯塞勒基金会）；University of Trento（特伦托大学）
Probabilistic 3D point cloud registration methods have shown competitive performance in overcoming noise, outliers, and density variations. However, registering point cloud pairs in the case of partial overlap is still a challenge. This paper proposes a novel overlap-guided probabilistic registration approach that computes the optimal transformation from matched Gaussian Mixture Model (GMM) parameters. We reformulate the registration problem as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We intro…
Centre Hospitalier de Luxembourg（卢森堡医院）；University of Luxembourg（卢森堡大学）；Zuse Institute Berlin（柏林楚泽研究所）；shapes GmbH（1000shapes有限责任公司）；Trier University of Applied Sciences（特里尔应用技术大学）
The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose…
UGD: An Unsupervised Geometric Distance for Evaluating Real-world Noisy Point Cloud Denoising
School of Automation, Nanjing University of Science and Technology（自动化学院，南京理工大学）；School of Computer Science and Engineering, Nanjing University of Science and Technology（计算机科学与工程学院，南京理工大学）
An $\varepsilon$-coreset for a given set $D$ of $n$ points, is usually a small weighted set, such that querying the coreset \emph{provably} yields a $(1+\varepsilon)$-factor approximation to the original (full) dataset, for a given family of queries. Using existing techniques, coresets can be maintained for streaming, dynamic (insertion/deletions), and distributed data in parallel, e.g. on a network, GPU or cloud. We suggest the first coresets that approximate the negative log-likelihood for $k$-Gaussians Mixture Models (GMM) of arbitrary shapes (ratio between eigenvalues of their covariance m…
When fitting Gaussian Mixture Models to 3D geometry, the model is typically fit to point clouds, even when the shapes were obtained as 3D meshes. Here we present a formulation for fitting Gaussian Mixture Models (GMMs) directly to a triangular mesh instead of using points sampled from its surface. Part of this work analyzes a general formulation for evaluating likelihood of geometric objects. This modification enables fitting higher-quality GMMs under a wider range of initialization conditions. Additionally, models obtained from this fitting method are shown to produce an improvement in 3D reg…
Point cloud registration is a fundamental problem in 3D computer vision, graphics and robotics. For the last few decades, existing registration algorithms have struggled in situations with large transformations, noise, and time constraints. In this paper, we introduce Deep Gaussian Mixture Registration (DeepGMR), the first learning-based registration method that explicitly leverages a probabilistic registration paradigm by formulating registration as the minimization of KL-divergence between two probability distributions modeled as mixtures of Gaussians. We design a neural network that extract…
In multimodal traffic monitoring, we gather traffic statistics for distinct transportation modes, such as pedestrians, cars and bicycles, in order to analyze and improve people's daily mobility in terms of safety and convenience. On account of its robustness to bad light and adverse weather conditions, and inherent speed measurement ability, the radar sensor is a suitable option for this application. However, the sparse radar data from conventional commercial radars make it extremely challenging for transportation mode classification. Thus, we propose to use a high-resolution millimeter-wave(m…
We present an iterative overlap estimation technique to augment existing point cloud registration algorithms that can achieve high performance in difficult real-world situations where large pose displacement and non-overlapping geometry would otherwise cause traditional methods to fail. Our approach estimates overlapping regions through an iterative Expectation Maximization procedure that encodes the sensor field-of-view into the registration process. The proposed technique, Expected Overlap Estimation (EOE), is derived from the observation that differences in field-of-view violate the iid ass…
This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and adaptive methods have been proposed to address the challenge of balancing model fidelity with size. Instead, state-of-the-art mapping approaches require tuning parameters for specific use cases, but do not generalize across diverse environments. To address this gap, we utilize a self-organizing principle from information-theoretic learning to automatically adap…
Unsupervised Change Detection for Space Habitats Using 3D Point Clouds
Chalmers University（查尔姆斯理工大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Stanford University（斯坦福大学）；CSIRO（联邦科学与工业研究组织）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）
